Modular C
C◼F257◼Z—17: symbols inserted from C◼snippet◼modulo.
+ Collaboration diagram for C◼F257◼Z—17: symbols inserted from C◼snippet◼modulo.:
typedef _Intern◼_I584Rsma◼C◼F257◼Z—17◼type₀ C◼F257◼𝔽—17
 
C◼F257◼𝔽—17 C◼F257◼generator—17 = C◼snippet◼modulo◼generator_default
 A generator of the multiplicative group. More...
 
C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—bnotbnot (C◼F257◼𝔽—17 a)
 Map a into ℤn. More...
 
C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—add (C◼F257◼𝔽—17 a, C◼F257◼𝔽—17 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—sub (C◼F257◼𝔽—17 a, C◼F257◼𝔽—17 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—prod (C◼F257◼𝔽—17 a, C◼F257◼𝔽—17 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—div (C◼F257◼𝔽—17 a, C◼F257◼𝔽—17 b)
 Operation in the ring ℤn. More...
 
C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—mod (C◼F257◼𝔽—17 a, C◼F257◼𝔽—17 b)
 Operation in the ring ℤn. More...
 
_Bool C◼F257◼𝔽—17◼_Operator—eq (C◼F257◼𝔽—17 a, C◼F257◼𝔽—17 b)
 Equality in the ring ℤn. More...
 
C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—notnot (C◼F257◼𝔽—17 a)
 Test if non-zero in ℤn. More...
 
C◼F257◼𝔽—17 C◼F257◼order—17 (C◼F257◼𝔽—17 x)
 Compute the order of element . More...
 

Detailed Description

See also
C◼snippet◼modulo snippet: identifiers inserted directly to an importer for details
This import uses the following slot(s)
slotreplacement
C◼snippet◼modulo◼modC◼F257◼MOD—17
C◼snippet◼modulo◼contextC◼F257◼𝔽—17
C◼snippet◼modulo◼typeC◼F257◼𝔽—17
C◼snippet◼modulo◼orderC◼F257◼order—17
C◼snippet◼modulo◼generatorC◼F257◼generator—17
C◼snippet◼modulo◼generator_defaultuses default

Typedef Documentation

§ C◼F257◼𝔽—17

typedef _Intern◼_I584Rsma◼C◼F257◼Z—17◼type₀ C◼F257◼𝔽—17

Definition at line 12912 of file C-F257.c.

Function Documentation

§ C◼F257◼order—17()

C◼F257◼𝔽—17 C◼F257◼order—17 ( C◼F257◼𝔽—17  x)

Compute the order of element .

The order is the smallest number r such that $x^{r} \mod n$.

Definition at line 12991 of file C-F257.c.

References C◼F257◼𝔽—17◼_Operator—add(), C◼F257◼𝔽—17◼_Operator—eq(), C◼F257◼𝔽—17◼_Operator—notnot(), and C◼F257◼𝔽—17◼_Operator—prod().

12991  {
12992 #line 147 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
12993  if (¬(C◼F257◼𝔽—17◼_Operator—notnot(x ))) return 0;
12994  C◼F257◼𝔽—17 y = x;
12995  for (C◼F257◼𝔽—17 i = 1; i; ((i )=(C◼F257◼𝔽—17◼_Operator—add(i , 1)))) {
12996 #line 150 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
12997  if (C◼F257◼𝔽—17◼_Operator—eq(y , 1 )) return i;
12998  ((y )=(C◼F257◼𝔽—17◼_Operator—prod(y , x )));
12999  }
13000  // should not be reached
13001  return 0;
13002 }
C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—prod(C◼F257◼𝔽—17 a, C◼F257◼𝔽—17 b)
Operation in the ring ℤn.
Definition: C-F257.c:12953
_Intern◼_I584Rsma◼C◼F257◼Z—17◼type₀ C◼F257◼𝔽—17
Definition: C-F257.c:12912
C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—notnot(C◼F257◼𝔽—17 a)
Test if non-zero in ℤn.
Definition: C-F257.c:12975
C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—add(C◼F257◼𝔽—17 a, C◼F257◼𝔽—17 b)
Operation in the ring ℤn.
Definition: C-F257.c:12941
_Bool C◼F257◼𝔽—17◼_Operator—eq(C◼F257◼𝔽—17 a, C◼F257◼𝔽—17 b)
Equality in the ring ℤn.
Definition: C-F257.c:12970
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§ C◼F257◼𝔽—17◼_Operator—add()

C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—add ( C◼F257◼𝔽—17  a,
C◼F257◼𝔽—17  b 
)
inline

Operation in the ring ℤn.

Definition at line 12941 of file C-F257.c.

References C◼F257◼𝔽—17◼_Operator—bnotbnot().

Referenced by C◼F257◼order—17().

12941  {
12942 #line 107 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
12943  C◼F257◼𝔽—17 ret = a + b;
12945 }
_Intern◼_I584Rsma◼C◼F257◼Z—17◼type₀ C◼F257◼𝔽—17
Definition: C-F257.c:12912
C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—bnotbnot(C◼F257◼𝔽—17 a)
Map a into ℤn.
Definition: C-F257.c:12936
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§ C◼F257◼𝔽—17◼_Operator—bnotbnot()

C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—bnotbnot ( C◼F257◼𝔽—17  a)
inline

Map a into ℤn.

Definition at line 12936 of file C-F257.c.

Referenced by C◼F257◼𝔽—17◼_Operator—add(), C◼F257◼𝔽—17◼_Operator—eq(), and C◼F257◼𝔽—17◼_Operator—prod().

12936  {
12937 #line 103 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
12938  return a % _Intern◼_I584Rsma◼C◼F257◼Z—17◼mod₀;
12939 }
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§ C◼F257◼𝔽—17◼_Operator—div()

C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—div ( C◼F257◼𝔽—17  a,
C◼F257◼𝔽—17  b 
)
inline

Operation in the ring ℤn.

Definition at line 12959 of file C-F257.c.

Referenced by C◼F257◼𝔽—17◼_Operator—mod().

12959  {
12960 #line 122 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
12961  C◼F257◼𝔽—17 ret = a * _Intern◼_I584Rsma◼C◼F257◼Z—17◼inverse(b);
12963 }
_Intern◼_I584Rsma◼C◼F257◼Z—17◼type₀ C◼F257◼𝔽—17
Definition: C-F257.c:12912
C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—bnotbnot(C◼F257◼𝔽—17 a)
Map a into ℤn.
Definition: C-F257.c:12936
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§ C◼F257◼𝔽—17◼_Operator—eq()

_Bool C◼F257◼𝔽—17◼_Operator—eq ( C◼F257◼𝔽—17  a,
C◼F257◼𝔽—17  b 
)
inline

Equality in the ring ℤn.

Definition at line 12970 of file C-F257.c.

References C◼F257◼𝔽—17◼_Operator—bnotbnot().

Referenced by C◼F257◼order—17().

12970  {
12971 #line 131 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
12973 }
C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—bnotbnot(C◼F257◼𝔽—17 a)
Map a into ℤn.
Definition: C-F257.c:12936
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§ C◼F257◼𝔽—17◼_Operator—mod()

C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—mod ( C◼F257◼𝔽—17  a,
C◼F257◼𝔽—17  b 
)
inline

Operation in the ring ℤn.

Definition at line 12965 of file C-F257.c.

References C◼F257◼𝔽—17◼_Operator—div(), C◼F257◼𝔽—17◼_Operator—prod(), and C◼F257◼𝔽—17◼_Operator—sub().

12965  {
12966 #line 127 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
12968 }
C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—div(C◼F257◼𝔽—17 a, C◼F257◼𝔽—17 b)
Operation in the ring ℤn.
Definition: C-F257.c:12959
C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—prod(C◼F257◼𝔽—17 a, C◼F257◼𝔽—17 b)
Operation in the ring ℤn.
Definition: C-F257.c:12953
C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—sub(C◼F257◼𝔽—17 a, C◼F257◼𝔽—17 b)
Operation in the ring ℤn.
Definition: C-F257.c:12947
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§ C◼F257◼𝔽—17◼_Operator—notnot()

C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—notnot ( C◼F257◼𝔽—17  a)
inline

Test if non-zero in ℤn.

Definition at line 12975 of file C-F257.c.

Referenced by C◼F257◼order—17().

12975  {
12976 #line 135 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
12977  return ‼C◼F257◼𝔽—17◼_Operator—bnotbnot(a);
12978 }
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§ C◼F257◼𝔽—17◼_Operator—prod()

C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—prod ( C◼F257◼𝔽—17  a,
C◼F257◼𝔽—17  b 
)
inline

Operation in the ring ℤn.

Definition at line 12953 of file C-F257.c.

References C◼F257◼𝔽—17◼_Operator—bnotbnot().

Referenced by C◼F257◼order—17(), and C◼F257◼𝔽—17◼_Operator—mod().

12953  {
12954 #line 117 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
12955  C◼F257◼𝔽—17 ret = a * b;
12957 }
_Intern◼_I584Rsma◼C◼F257◼Z—17◼type₀ C◼F257◼𝔽—17
Definition: C-F257.c:12912
C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—bnotbnot(C◼F257◼𝔽—17 a)
Map a into ℤn.
Definition: C-F257.c:12936
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§ C◼F257◼𝔽—17◼_Operator—sub()

C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—sub ( C◼F257◼𝔽—17  a,
C◼F257◼𝔽—17  b 
)
inline

Operation in the ring ℤn.

Definition at line 12947 of file C-F257.c.

Referenced by C◼F257◼𝔽—17◼_Operator—mod().

12947  {
12948 #line 112 "/home/gustedt/build/cmod/C/C-snippet-modulo.X"
12949  C◼F257◼𝔽—17 ret = a + (_Intern◼_I584Rsma◼C◼F257◼Z—17◼mod₀ - b);
12951 }
_Intern◼_I584Rsma◼C◼F257◼Z—17◼type₀ C◼F257◼𝔽—17
Definition: C-F257.c:12912
C◼F257◼𝔽—17 C◼F257◼𝔽—17◼_Operator—bnotbnot(C◼F257◼𝔽—17 a)
Map a into ℤn.
Definition: C-F257.c:12936
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Variable Documentation

§ C◼F257◼generator—17

A generator of the multiplicative group.

Remarks
This will only be computed automatically at program startup, if ◼C◼snippet◼modulo◼max_find is set to a high enough value.

Definition at line 13011 of file C-F257.c.